Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(3025,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.3025");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\Q(\zeta_{40})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{12} + x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{8} \) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3025.15 | ||
Root | \(-0.156434 + 0.987688i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.3025 |
Dual form | 6048.2.c.d.3025.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.29757i | 1.92193i | 0.276666 | + | 0.960966i | \(0.410770\pi\) | ||||
−0.276666 | + | 0.960966i | \(0.589230\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 1.60758i | − 0.484703i | −0.970189 | − | 0.242351i | \(-0.922081\pi\) | ||||
0.970189 | − | 0.242351i | \(-0.0779187\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 6.02967i | − 1.67233i | −0.548478 | − | 0.836165i | \(-0.684792\pi\) | ||||
0.548478 | − | 0.836165i | \(-0.315208\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.16228 | −0.766965 | −0.383482 | − | 0.923548i | \(-0.625275\pi\) | ||||
−0.383482 | + | 0.923548i | \(0.625275\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.07768i | 0.706069i | 0.935610 | + | 0.353035i | \(0.114850\pi\) | ||||
−0.935610 | + | 0.353035i | \(0.885150\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.95080 | 1.24083 | 0.620413 | − | 0.784275i | \(-0.286965\pi\) | ||||
0.620413 | + | 0.784275i | \(0.286965\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −13.4691 | −2.69382 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 3.53972i | − 0.657310i | −0.944450 | − | 0.328655i | \(-0.893405\pi\) | ||||
0.944450 | − | 0.328655i | \(-0.106595\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.08831 | 0.375071 | 0.187535 | − | 0.982258i | \(-0.439950\pi\) | ||||
0.187535 | + | 0.982258i | \(0.439950\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.29757i | 0.726422i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 4.48276i | − 0.736961i | −0.929636 | − | 0.368480i | \(-0.879878\pi\) | ||||
0.929636 | − | 0.368480i | \(-0.120122\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.69568 | 1.04569 | 0.522845 | − | 0.852428i | \(-0.324871\pi\) | ||||
0.522845 | + | 0.852428i | \(0.324871\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 12.2811i | − 1.87284i | −0.350875 | − | 0.936422i | \(-0.614116\pi\) | ||||
0.350875 | − | 0.936422i | \(-0.385884\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.82734 | 0.558275 | 0.279138 | − | 0.960251i | \(-0.409951\pi\) | ||||
0.279138 | + | 0.960251i | \(0.409951\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 8.63711i | − 1.18640i | −0.805056 | − | 0.593199i | \(-0.797865\pi\) | ||||
0.805056 | − | 0.593199i | \(-0.202135\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.90868 | 0.931566 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.55265i | 0.202137i | 0.994879 | + | 0.101069i | \(0.0322262\pi\) | ||||
−0.994879 | + | 0.101069i | \(0.967774\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 3.64886i | − 0.467189i | −0.972334 | − | 0.233594i | \(-0.924951\pi\) | ||||
0.972334 | − | 0.233594i | \(-0.0750487\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 25.9129 | 3.21411 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.772361i | 0.0943590i | 0.998886 | + | 0.0471795i | \(0.0150233\pi\) | ||||
−0.998886 | + | 0.0471795i | \(0.984977\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.36501 | 0.874066 | 0.437033 | − | 0.899446i | \(-0.356029\pi\) | ||||
0.437033 | + | 0.899446i | \(0.356029\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.32739 | 0.155359 | 0.0776797 | − | 0.996978i | \(-0.475249\pi\) | ||||
0.0776797 | + | 0.996978i | \(0.475249\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.60758i | − 0.183200i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.7401 | −1.43337 | −0.716685 | − | 0.697397i | \(-0.754341\pi\) | ||||
−0.716685 | + | 0.697397i | \(0.754341\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 7.08446i | − 0.777620i | −0.921318 | − | 0.388810i | \(-0.872886\pi\) | ||||
0.921318 | − | 0.388810i | \(-0.127114\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 13.5901i | − 1.47405i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.73307 | −1.03170 | −0.515852 | − | 0.856678i | \(-0.672525\pi\) | ||||
−0.515852 | + | 0.856678i | \(0.672525\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 6.02967i | − 0.632081i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −13.2266 | −1.35702 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.1803 | −1.03366 | −0.516828 | − | 0.856089i | \(-0.672887\pi\) | ||||
−0.516828 | + | 0.856089i | \(0.672887\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.02749i | 0.102239i | 0.998693 | + | 0.0511194i | \(0.0162789\pi\) | ||||
−0.998693 | + | 0.0511194i | \(0.983721\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.965118 | 0.0950959 | 0.0475479 | − | 0.998869i | \(-0.484859\pi\) | ||||
0.0475479 | + | 0.998869i | \(0.484859\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.0949i | 1.55595i | 0.628294 | + | 0.777976i | \(0.283754\pi\) | ||||
−0.628294 | + | 0.777976i | \(0.716246\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 20.2686i | − 1.94138i | −0.240327 | − | 0.970692i | \(-0.577255\pi\) | ||||
0.240327 | − | 0.970692i | \(-0.422745\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.951214 | 0.0894826 | 0.0447413 | − | 0.998999i | \(-0.485754\pi\) | ||||
0.0447413 | + | 0.998999i | \(0.485754\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 25.5740i | 2.38478i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.16228 | −0.289886 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.41570 | 0.765063 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 36.3966i | − 3.25541i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.6132 | 1.03050 | 0.515250 | − | 0.857040i | \(-0.327699\pi\) | ||||
0.515250 | + | 0.857040i | \(0.327699\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 10.0120i | − 0.874752i | −0.899279 | − | 0.437376i | \(-0.855908\pi\) | ||||
0.899279 | − | 0.437376i | \(-0.144092\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.07768i | 0.266869i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.40383 | 0.717988 | 0.358994 | − | 0.933340i | \(-0.383120\pi\) | ||||
0.358994 | + | 0.933340i | \(0.383120\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 6.61437i | − 0.561024i | −0.959851 | − | 0.280512i | \(-0.909496\pi\) | ||||
0.959851 | − | 0.280512i | \(-0.0905042\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.69316 | −0.810583 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.2122 | 1.26330 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 16.9866i | − 1.39160i | −0.718238 | − | 0.695798i | \(-0.755051\pi\) | ||||
0.718238 | − | 0.695798i | \(-0.244949\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.5256 | 0.937937 | 0.468968 | − | 0.883215i | \(-0.344626\pi\) | ||||
0.468968 | + | 0.883215i | \(0.344626\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.97464i | 0.720860i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.3889i | 0.829127i | 0.910020 | + | 0.414563i | \(0.136066\pi\) | ||||
−0.910020 | + | 0.414563i | \(0.863934\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.95080 | 0.468988 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.8743i | 0.930067i | 0.885293 | + | 0.465034i | \(0.153958\pi\) | ||||
−0.885293 | + | 0.465034i | \(0.846042\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.0596 | 1.16535 | 0.582673 | − | 0.812706i | \(-0.302007\pi\) | ||||
0.582673 | + | 0.812706i | \(0.302007\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.3570 | −1.79669 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.7854i | 1.80837i | 0.427142 | + | 0.904185i | \(0.359521\pi\) | ||||
−0.427142 | + | 0.904185i | \(0.640479\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.4691 | −1.01817 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 22.1919i | − 1.65870i | −0.558728 | − | 0.829351i | \(-0.688710\pi\) | ||||
0.558728 | − | 0.829351i | \(-0.311290\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 8.60253i | − 0.639421i | −0.947515 | − | 0.319711i | \(-0.896414\pi\) | ||||
0.947515 | − | 0.319711i | \(-0.103586\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 19.2650 | 1.41639 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.08361i | 0.371750i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.72989 | −0.631673 | −0.315836 | − | 0.948814i | \(-0.602285\pi\) | ||||
−0.315836 | + | 0.948814i | \(0.602285\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.8708 | −0.926459 | −0.463229 | − | 0.886238i | \(-0.653309\pi\) | ||||
−0.463229 | + | 0.886238i | \(0.653309\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.4345i | 1.59839i | 0.601072 | + | 0.799195i | \(0.294741\pi\) | ||||
−0.601072 | + | 0.799195i | \(0.705259\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.9799 | 1.06189 | 0.530947 | − | 0.847405i | \(-0.321836\pi\) | ||||
0.530947 | + | 0.847405i | \(0.321836\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 3.53972i | − 0.248440i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 28.7752i | 2.00974i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.94761 | 0.342234 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.50651i | 0.585612i | 0.956172 | + | 0.292806i | \(0.0945890\pi\) | ||||
−0.956172 | + | 0.292806i | \(0.905411\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 52.7787 | 3.59948 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.08831 | 0.141763 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.0675i | 1.28262i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.3214 | −1.09296 | −0.546479 | − | 0.837473i | \(-0.684032\pi\) | ||||
−0.546479 | + | 0.837473i | \(0.684032\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.8279i | 0.718671i | 0.933208 | + | 0.359336i | \(0.116997\pi\) | ||||
−0.933208 | + | 0.359336i | \(0.883003\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.9251i | 1.64710i | 0.567245 | + | 0.823549i | \(0.308009\pi\) | ||||
−0.567245 | + | 0.823549i | \(0.691991\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.5950 | 0.890641 | 0.445321 | − | 0.895371i | \(-0.353090\pi\) | ||||
0.445321 | + | 0.895371i | \(0.353090\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.4483i | 1.07297i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.82998 | 0.247741 | 0.123870 | − | 0.992298i | \(-0.460469\pi\) | ||||
0.123870 | + | 0.992298i | \(0.460469\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.32509 | 0.343019 | 0.171509 | − | 0.985182i | \(-0.445136\pi\) | ||||
0.171509 | + | 0.985182i | \(0.445136\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.29757i | 0.274562i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.5574 | 1.18078 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 19.2193i | − 1.21311i | −0.795040 | − | 0.606556i | \(-0.792550\pi\) | ||||
0.795040 | − | 0.606556i | \(-0.207450\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 9.56636i | − 0.601432i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.655642 | −0.0408979 | −0.0204489 | − | 0.999791i | \(-0.506510\pi\) | ||||
−0.0204489 | + | 0.999791i | \(0.506510\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 4.48276i | − 0.278545i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.8211 | 1.59220 | 0.796098 | − | 0.605168i | \(-0.206894\pi\) | ||||
0.796098 | + | 0.605168i | \(0.206894\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 37.1186 | 2.28018 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 14.2078i | − 0.866266i | −0.901330 | − | 0.433133i | \(-0.857408\pi\) | ||||
0.901330 | − | 0.433133i | \(-0.142592\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.52786 | −0.214302 | −0.107151 | − | 0.994243i | \(-0.534173\pi\) | ||||
−0.107151 | + | 0.994243i | \(0.534173\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 21.6526i | 1.30570i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 13.9396i | − 0.837548i | −0.908091 | − | 0.418774i | \(-0.862460\pi\) | ||||
0.908091 | − | 0.418774i | \(-0.137540\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.4105 | −1.21759 | −0.608793 | − | 0.793329i | \(-0.708346\pi\) | ||||
−0.608793 | + | 0.793329i | \(0.708346\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 29.6867i | 1.76469i | 0.470600 | + | 0.882347i | \(0.344037\pi\) | ||||
−0.470600 | + | 0.882347i | \(0.655963\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.69568 | 0.395233 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.4504i | 0.961044i | 0.876983 | + | 0.480522i | \(0.159553\pi\) | ||||
−0.876983 | + | 0.480522i | \(0.840447\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.67261 | −0.388494 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 35.8813i | − 2.07507i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 12.2811i | − 0.707869i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.6812 | 0.897905 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 19.8393i | − 1.13229i | −0.824306 | − | 0.566145i | \(-0.808434\pi\) | ||||
0.824306 | − | 0.566145i | \(-0.191566\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 32.3919 | 1.83677 | 0.918387 | − | 0.395683i | \(-0.129492\pi\) | ||||
0.918387 | + | 0.395683i | \(0.129492\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.02156 | −0.340359 | −0.170179 | − | 0.985413i | \(-0.554435\pi\) | ||||
−0.170179 | + | 0.985413i | \(0.554435\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.23318i | 0.293925i | 0.989142 | + | 0.146962i | \(0.0469496\pi\) | ||||
−0.989142 | + | 0.146962i | \(0.953050\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.69038 | −0.318600 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 9.73249i | − 0.541530i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 81.2144i | 4.50496i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.82734 | 0.211008 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.5740i | 0.910988i | 0.890239 | + | 0.455494i | \(0.150537\pi\) | ||||
−0.890239 | + | 0.455494i | \(0.849463\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.31928 | −0.181352 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.70020 | 0.0926159 | 0.0463080 | − | 0.998927i | \(-0.485254\pi\) | ||||
0.0463080 | + | 0.998927i | \(0.485254\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 3.35711i | − 0.181798i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.0032i | 1.28856i | 0.764790 | + | 0.644279i | \(0.222843\pi\) | ||||
−0.764790 | + | 0.644279i | \(0.777157\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.3679i | 1.14380i | 0.820324 | + | 0.571898i | \(0.193793\pi\) | ||||
−0.820324 | + | 0.571898i | \(0.806207\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.1560 | −1.33892 | −0.669460 | − | 0.742849i | \(-0.733474\pi\) | ||||
−0.669460 | + | 0.742849i | \(0.733474\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 31.6517i | 1.67990i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.1318 | −0.956957 | −0.478479 | − | 0.878099i | \(-0.658812\pi\) | ||||
−0.478479 | + | 0.878099i | \(0.658812\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.52786 | 0.501467 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.70456i | 0.298590i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 29.6249 | 1.54641 | 0.773203 | − | 0.634158i | \(-0.218653\pi\) | ||||
0.773203 | + | 0.634158i | \(0.218653\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 8.63711i | − 0.448416i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 29.3696i | − 1.52070i | −0.649514 | − | 0.760349i | \(-0.725028\pi\) | ||||
0.649514 | − | 0.760349i | \(-0.274972\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −21.3434 | −1.09924 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 16.1375i | − 0.828930i | −0.910065 | − | 0.414465i | \(-0.863969\pi\) | ||||
0.910065 | − | 0.414465i | \(-0.136031\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.9227 | 1.12020 | 0.560099 | − | 0.828426i | \(-0.310763\pi\) | ||||
0.560099 | + | 0.828426i | \(0.310763\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.90868 | 0.352099 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 27.7725i | − 1.40812i | −0.710140 | − | 0.704061i | \(-0.751368\pi\) | ||||
0.710140 | − | 0.704061i | \(-0.248632\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.8181 | −0.951671 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 54.7514i | − 2.75484i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 27.6193i | − 1.38617i | −0.720855 | − | 0.693086i | \(-0.756251\pi\) | ||||
0.720855 | − | 0.693086i | \(-0.243749\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.4439 | −0.521546 | −0.260773 | − | 0.965400i | \(-0.583977\pi\) | ||||
−0.260773 | + | 0.965400i | \(0.583977\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 12.5918i | − 0.627242i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.20638 | −0.357207 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.1424 | 0.748745 | 0.374373 | − | 0.927278i | \(-0.377858\pi\) | ||||
0.374373 | + | 0.927278i | \(0.377858\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.55265i | 0.0764007i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 30.4460 | 1.49453 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.9623i | 0.975222i | 0.873061 | + | 0.487611i | \(0.162131\pi\) | ||||
−0.873061 | + | 0.487611i | \(0.837869\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 12.8339i | − 0.625486i | −0.949838 | − | 0.312743i | \(-0.898752\pi\) | ||||
0.949838 | − | 0.312743i | \(-0.101248\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 42.5931 | 2.06607 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 3.64886i | − 0.176581i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.66364 | −0.128303 | −0.0641514 | − | 0.997940i | \(-0.520434\pi\) | ||||
−0.0641514 | + | 0.997940i | \(0.520434\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.2122 | −0.923280 | −0.461640 | − | 0.887067i | \(-0.652739\pi\) | ||||
−0.461640 | + | 0.887067i | \(0.652739\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.3147i | 0.876109i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 35.1209 | 1.67623 | 0.838114 | − | 0.545495i | \(-0.183658\pi\) | ||||
0.838114 | + | 0.545495i | \(0.183658\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 8.40943i | − 0.399544i | −0.979842 | − | 0.199772i | \(-0.935980\pi\) | ||||
0.979842 | − | 0.199772i | \(-0.0640202\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 41.8286i | − 1.98286i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.81067 | 0.227030 | 0.113515 | − | 0.993536i | \(-0.463789\pi\) | ||||
0.113515 | + | 0.993536i | \(0.463789\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 10.7638i | − 0.506848i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 25.9129 | 1.21482 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −37.8291 | −1.76957 | −0.884785 | − | 0.465999i | \(-0.845695\pi\) | ||||
−0.884785 | + | 0.465999i | \(0.845695\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.5113i | 0.489558i | 0.969579 | + | 0.244779i | \(0.0787154\pi\) | ||||
−0.969579 | + | 0.244779i | \(0.921285\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.76163 | −0.221292 | −0.110646 | − | 0.993860i | \(-0.535292\pi\) | ||||
−0.110646 | + | 0.993860i | \(0.535292\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 19.7216i | − 0.912609i | −0.889824 | − | 0.456305i | \(-0.849173\pi\) | ||||
0.889824 | − | 0.456305i | \(-0.150827\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.772361i | 0.0356643i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19.7428 | −0.907773 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 41.4537i | − 1.90203i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.49558 | 0.114026 | 0.0570131 | − | 0.998373i | \(-0.481842\pi\) | ||||
0.0570131 | + | 0.998373i | \(0.481842\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.0296 | −1.23244 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 43.7507i | − 1.98662i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.0178 | 0.453951 | 0.226976 | − | 0.973900i | \(-0.427116\pi\) | ||||
0.226976 | + | 0.973900i | \(0.427116\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.23469i | 0.191109i | 0.995424 | + | 0.0955544i | \(0.0304624\pi\) | ||||
−0.995424 | + | 0.0955544i | \(0.969538\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.1936i | 0.504134i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.36501 | 0.330366 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.1176i | 0.452925i | 0.974020 | + | 0.226463i | \(0.0727161\pi\) | ||||
−0.974020 | + | 0.226463i | \(0.927284\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.6693 | 0.966186 | 0.483093 | − | 0.875569i | \(-0.339513\pi\) | ||||
0.483093 | + | 0.875569i | \(0.339513\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.41570 | −0.196496 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 13.8362i | − 0.613280i | −0.951826 | − | 0.306640i | \(-0.900795\pi\) | ||||
0.951826 | − | 0.306640i | \(-0.0992048\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.32739 | 0.0587203 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.14766i | 0.182768i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 6.15275i | − 0.270597i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.5067 | 0.854603 | 0.427302 | − | 0.904109i | \(-0.359464\pi\) | ||||
0.427302 | + | 0.904109i | \(0.359464\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 0.616566i | − 0.0269606i | −0.999909 | − | 0.0134803i | \(-0.995709\pi\) | ||||
0.999909 | − | 0.0134803i | \(-0.00429104\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.60380 | −0.287666 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.4120 | 0.539651 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 40.3727i | − 1.74874i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −69.1690 | −2.99044 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 1.60758i | − 0.0692433i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.0638i | 1.42152i | 0.703432 | + | 0.710762i | \(0.251650\pi\) | ||||
−0.703432 | + | 0.710762i | \(0.748350\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 87.1059 | 3.73121 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 45.6463i | − 1.95170i | −0.218450 | − | 0.975848i | \(-0.570100\pi\) | ||||
0.218450 | − | 0.975848i | \(-0.429900\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.8941 | 0.464106 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.7401 | −0.541763 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 0.0518694i | − 0.00219778i | −0.999999 | − | 0.00109889i | \(-0.999650\pi\) | ||||
0.999999 | − | 0.00109889i | \(-0.000349787\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −74.0508 | −3.13201 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 10.9105i | − 0.459822i | −0.973212 | − | 0.229911i | \(-0.926156\pi\) | ||||
0.973212 | − | 0.229911i | \(-0.0738436\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.08791i | 0.171980i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.2746 | 1.10149 | 0.550745 | − | 0.834673i | \(-0.314344\pi\) | ||||
0.550745 | + | 0.834673i | \(0.314344\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 24.4590i | − 1.02358i | −0.859111 | − | 0.511789i | \(-0.828983\pi\) | ||||
0.859111 | − | 0.511789i | \(-0.171017\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −80.1520 | −3.34257 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.2538 | −0.426873 | −0.213436 | − | 0.976957i | \(-0.568466\pi\) | ||||
−0.213436 | + | 0.976957i | \(0.568466\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 7.08446i | − 0.293913i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.8848 | −0.575050 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.3720i | 1.04722i | 0.851959 | + | 0.523608i | \(0.175414\pi\) | ||||
−0.851959 | + | 0.523608i | \(0.824586\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.42714i | 0.264826i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.14310 | −0.293332 | −0.146666 | − | 0.989186i | \(-0.546854\pi\) | ||||
−0.146666 | + | 0.989186i | \(0.546854\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 13.5901i | − 0.557140i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.00175 | 0.122648 | 0.0613242 | − | 0.998118i | \(-0.480468\pi\) | ||||
0.0613242 | + | 0.998118i | \(0.480468\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.2516 | 0.866871 | 0.433435 | − | 0.901185i | \(-0.357301\pi\) | ||||
0.433435 | + | 0.901185i | \(0.357301\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 36.1671i | 1.47040i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.0614 | −0.976623 | −0.488312 | − | 0.872669i | \(-0.662387\pi\) | ||||
−0.488312 | + | 0.872669i | \(0.662387\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 23.0776i | − 0.933620i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 20.9197i | − 0.844939i | −0.906377 | − | 0.422469i | \(-0.861163\pi\) | ||||
0.906377 | − | 0.422469i | \(-0.138837\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.95122 | −0.159070 | −0.0795350 | − | 0.996832i | \(-0.525344\pi\) | ||||
−0.0795350 | + | 0.996832i | \(0.525344\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 23.8651i | − 0.959220i | −0.877482 | − | 0.479610i | \(-0.840778\pi\) | ||||
0.877482 | − | 0.479610i | \(-0.159222\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.73307 | −0.389947 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 89.0716 | 3.56286 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.1757i | 0.565223i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.3725 | −1.44797 | −0.723983 | − | 0.689818i | \(-0.757690\pi\) | ||||
−0.723983 | + | 0.689818i | \(0.757690\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 49.9083i | 1.98055i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 6.02967i | − 0.238904i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.876669 | −0.0346264 | −0.0173132 | − | 0.999850i | \(-0.505511\pi\) | ||||
−0.0173132 | + | 0.999850i | \(0.505511\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 15.2486i | − 0.601347i | −0.953727 | − | 0.300674i | \(-0.902789\pi\) | ||||
0.953727 | − | 0.300674i | \(-0.0972114\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.53027 | −0.374673 | −0.187337 | − | 0.982296i | \(-0.559986\pi\) | ||||
−0.187337 | + | 0.982296i | \(0.559986\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.49600 | 0.0979765 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 9.29496i | − 0.363740i | −0.983323 | − | 0.181870i | \(-0.941785\pi\) | ||||
0.983323 | − | 0.181870i | \(-0.0582150\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 43.0273 | 1.68121 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.1879i | 1.40968i | 0.709366 | + | 0.704841i | \(0.248982\pi\) | ||||
−0.709366 | + | 0.704841i | \(0.751018\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.8091i | 0.770483i | 0.922816 | + | 0.385242i | \(0.125882\pi\) | ||||
−0.922816 | + | 0.385242i | \(0.874118\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −13.2266 | −0.512904 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 21.0642i | − 0.815607i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.86582 | −0.226448 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.186375 | −0.00718421 | −0.00359211 | − | 0.999994i | \(-0.501143\pi\) | ||||
−0.00359211 | + | 0.999994i | \(0.501143\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 3.31885i | − 0.127554i | −0.997964 | − | 0.0637770i | \(-0.979685\pi\) | ||||
0.997964 | − | 0.0637770i | \(-0.0203146\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.1803 | −0.390686 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.9992i | 0.688720i | 0.938838 | + | 0.344360i | \(0.111904\pi\) | ||||
−0.938838 | + | 0.344360i | \(0.888096\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 36.1161i | 1.37992i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −52.0789 | −1.98405 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 3.67153i | − 0.139671i | −0.997559 | − | 0.0698357i | \(-0.977752\pi\) | ||||
0.997559 | − | 0.0698357i | \(-0.0222475\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 28.4257 | 1.07825 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.1736 | −0.802007 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 7.06843i | − 0.266971i | −0.991051 | − | 0.133485i | \(-0.957383\pi\) | ||||
0.991051 | − | 0.133485i | \(-0.0426169\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.7965 | 0.520345 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.02749i | 0.0386426i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 20.4607i | − 0.768417i | −0.923246 | − | 0.384209i | \(-0.874474\pi\) | ||||
0.923246 | − | 0.384209i | \(-0.125526\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.4271 | 0.465398 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 41.6571i | − 1.55789i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.5191 | −1.51111 | −0.755554 | − | 0.655087i | \(-0.772632\pi\) | ||||
−0.755554 | + | 0.655087i | \(0.772632\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.965118 | 0.0359429 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 47.6769i | 1.77068i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.87078 | −0.254823 | −0.127412 | − | 0.991850i | \(-0.540667\pi\) | ||||
−0.127412 | + | 0.991850i | \(0.540667\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 38.8361i | 1.43641i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 18.5847i | − 0.686442i | −0.939255 | − | 0.343221i | \(-0.888482\pi\) | ||||
0.939255 | − | 0.343221i | \(-0.111518\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.24163 | 0.0457360 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.69519i | 0.172715i | 0.996264 | + | 0.0863576i | \(0.0275228\pi\) | ||||
−0.996264 | + | 0.0863576i | \(0.972477\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.5867 | −0.571821 | −0.285911 | − | 0.958256i | \(-0.592296\pi\) | ||||
−0.285911 | + | 0.958256i | \(0.592296\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 73.0011 | 2.67455 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.0949i | 0.588095i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.7401 | 0.683835 | 0.341917 | − | 0.939730i | \(-0.388924\pi\) | ||||
0.341917 | + | 0.939730i | \(0.388924\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 49.5319i | 1.80265i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 24.9095i | − 0.905352i | −0.891675 | − | 0.452676i | \(-0.850469\pi\) | ||||
0.891675 | − | 0.452676i | \(-0.149531\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.70991 | −0.170734 | −0.0853670 | − | 0.996350i | \(-0.527206\pi\) | ||||
−0.0853670 | + | 0.996350i | \(0.527206\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 20.2686i | − 0.733774i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.36195 | 0.338040 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.8989 | 0.501208 | 0.250604 | − | 0.968090i | \(-0.419371\pi\) | ||||
0.250604 | + | 0.968090i | \(0.419371\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.8995i | 0.535899i | 0.963433 | + | 0.267949i | \(0.0863460\pi\) | ||||
−0.963433 | + | 0.267949i | \(0.913654\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28.1276 | −1.01037 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.6072i | 0.738329i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 11.8398i | − 0.423662i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −44.6472 | −1.59353 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.1839i | 0.363018i | 0.983389 | + | 0.181509i | \(0.0580981\pi\) | ||||
−0.983389 | + | 0.181509i | \(0.941902\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.951214 | 0.0338213 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −22.0014 | −0.781293 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.0210i | 0.496648i | 0.968677 | + | 0.248324i | \(0.0798798\pi\) | ||||
−0.968677 | + | 0.248324i | \(0.920120\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.1031 | −0.428177 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 2.13388i | − 0.0753031i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25.5740i | 0.901364i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.0399 | −0.985831 | −0.492916 | − | 0.870077i | \(-0.664069\pi\) | ||||
−0.492916 | + | 0.870077i | \(0.664069\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 13.2362i | − 0.464785i | −0.972622 | − | 0.232393i | \(-0.925345\pi\) | ||||
0.972622 | − | 0.232393i | \(-0.0746554\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −51.0307 | −1.78753 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 37.7972 | 1.32236 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 13.8343i | − 0.482821i | −0.970423 | − | 0.241411i | \(-0.922390\pi\) | ||||
0.970423 | − | 0.241411i | \(-0.0776100\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.4862 | −1.02782 | −0.513912 | − | 0.857843i | \(-0.671804\pi\) | ||||
−0.513912 | + | 0.857843i | \(0.671804\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 28.9797i | − 1.00772i | −0.863784 | − | 0.503861i | \(-0.831912\pi\) | ||||
0.863784 | − | 0.503861i | \(-0.168088\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 32.5800i | − 1.13155i | −0.824560 | − | 0.565774i | \(-0.808577\pi\) | ||||
0.824560 | − | 0.565774i | \(-0.191423\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.16228 | −0.109566 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 64.7197i | 2.23972i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.8215 | 0.684313 | 0.342157 | − | 0.939643i | \(-0.388843\pi\) | ||||
0.342157 | + | 0.939643i | \(0.388843\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.4704 | 0.567944 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 100.378i | − 3.45311i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.41570 | 0.289167 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 26.6760i | − 0.914441i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.4764i | 0.598381i | 0.954193 | + | 0.299190i | \(0.0967166\pi\) | ||||
−0.954193 | + | 0.299190i | \(0.903283\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.0767 | −0.890764 | −0.445382 | − | 0.895341i | \(-0.646932\pi\) | ||||
−0.445382 | + | 0.895341i | \(0.646932\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 40.6339i | − 1.38641i | −0.720740 | − | 0.693205i | \(-0.756198\pi\) | ||||
0.720740 | − | 0.693205i | \(-0.243802\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.4216 | 1.41001 | 0.705004 | − | 0.709204i | \(-0.250945\pi\) | ||||
0.705004 | + | 0.709204i | \(0.250945\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −102.219 | −3.47556 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.4806i | 0.694758i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.65709 | 0.157799 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 36.3966i | − 1.23043i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.0093i | 1.11464i | 0.830296 | + | 0.557322i | \(0.188171\pi\) | ||||
−0.830296 | + | 0.557322i | \(0.811829\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.0587 | 0.608414 | 0.304207 | − | 0.952606i | \(-0.401609\pi\) | ||||
0.304207 | + | 0.952606i | \(0.401609\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46.6771i | 1.57081i | 0.618983 | + | 0.785404i | \(0.287545\pi\) | ||||
−0.618983 | + | 0.785404i | \(0.712455\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29.2001 | −0.980444 | −0.490222 | − | 0.871598i | \(-0.663084\pi\) | ||||
−0.490222 | + | 0.871598i | \(0.663084\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.6132 | 0.389493 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.7793i | 0.394181i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 95.3714 | 3.18791 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 7.39202i | − 0.246538i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.3129i | 0.909926i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 36.9700 | 1.22892 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 9.06592i | − 0.301029i | −0.988608 | − | 0.150514i | \(-0.951907\pi\) | ||||
0.988608 | − | 0.150514i | \(-0.0480930\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.3571 | −0.475673 | −0.237837 | − | 0.971305i | \(-0.576438\pi\) | ||||
−0.237837 | + | 0.971305i | \(0.576438\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.3888 | −0.376915 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 10.0120i | − 0.330625i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49.8788 | −1.64535 | −0.822675 | − | 0.568513i | \(-0.807519\pi\) | ||||
−0.822675 | + | 0.568513i | \(0.807519\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 44.4086i | − 1.46173i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 60.3788i | 1.98524i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.3069 | 1.28962 | 0.644809 | − | 0.764343i | \(-0.276937\pi\) | ||||
0.644809 | + | 0.764343i | \(0.276937\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.07768i | 0.100867i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −21.8472 | −0.714478 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.3504 | 1.22018 | 0.610092 | − | 0.792331i | \(-0.291133\pi\) | ||||
0.610092 | + | 0.792331i | \(0.291133\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.7781i | 1.26413i | 0.774915 | + | 0.632065i | \(0.217792\pi\) | ||||
−0.774915 | + | 0.632065i | \(0.782208\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39.8446 | 1.29752 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 3.75328i | − 0.121965i | −0.998139 | − | 0.0609826i | \(-0.980577\pi\) | ||||
0.998139 | − | 0.0609826i | \(-0.0194234\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 8.00373i | − 0.259812i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −46.5443 | −1.50772 | −0.753859 | − | 0.657036i | \(-0.771810\pi\) | ||||
−0.753859 | + | 0.657036i | \(0.771810\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 37.5173i | − 1.21403i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.40383 | 0.271374 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.6390 | −0.859322 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 55.3131i | − 1.78059i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.6487 | 0.535388 | 0.267694 | − | 0.963504i | \(-0.413738\pi\) | ||||
0.267694 | + | 0.963504i | \(0.413738\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 5.74652i | − 0.184415i | −0.995740 | − | 0.0922073i | \(-0.970608\pi\) | ||||
0.995740 | − | 0.0922073i | \(-0.0293922\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 6.61437i | − 0.212047i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27.6236 | −0.883758 | −0.441879 | − | 0.897075i | \(-0.645688\pi\) | ||||
−0.441879 | + | 0.897075i | \(0.645688\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.6467i | 0.500070i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.19812 | 0.0701091 | 0.0350545 | − | 0.999385i | \(-0.488840\pi\) | ||||
0.0350545 | + | 0.999385i | \(0.488840\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −96.4138 | −3.07200 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 73.0821i | − 2.32388i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.62346 | −0.0833369 | −0.0416684 | − | 0.999131i | \(-0.513267\pi\) | ||||
−0.0416684 | + | 0.999131i | \(0.513267\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 64.3770i | 2.04089i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 29.1361i | − 0.922749i | −0.887205 | − | 0.461375i | \(-0.847356\pi\) | ||||
0.887205 | − | 0.461375i | \(-0.152644\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6048.2.c.d.3025.15 | 16 | ||
3.2 | odd | 2 | inner | 6048.2.c.d.3025.1 | 16 | ||
4.3 | odd | 2 | 1512.2.c.d.757.8 | yes | 16 | ||
8.3 | odd | 2 | 1512.2.c.d.757.5 | ✓ | 16 | ||
8.5 | even | 2 | inner | 6048.2.c.d.3025.2 | 16 | ||
12.11 | even | 2 | 1512.2.c.d.757.9 | yes | 16 | ||
24.5 | odd | 2 | inner | 6048.2.c.d.3025.16 | 16 | ||
24.11 | even | 2 | 1512.2.c.d.757.12 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.d.757.5 | ✓ | 16 | 8.3 | odd | 2 | ||
1512.2.c.d.757.8 | yes | 16 | 4.3 | odd | 2 | ||
1512.2.c.d.757.9 | yes | 16 | 12.11 | even | 2 | ||
1512.2.c.d.757.12 | yes | 16 | 24.11 | even | 2 | ||
6048.2.c.d.3025.1 | 16 | 3.2 | odd | 2 | inner | ||
6048.2.c.d.3025.2 | 16 | 8.5 | even | 2 | inner | ||
6048.2.c.d.3025.15 | 16 | 1.1 | even | 1 | trivial | ||
6048.2.c.d.3025.16 | 16 | 24.5 | odd | 2 | inner |